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Hi,
I am wondering what mathematical formula is used to calculate growth of an investment if you have the percent return (or the doubling time of the investment). I could do it if there was a one time addition but what if you add a set amount each year (as in IRA contributions)?
Thanks,
Carson
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No. of Recommendations: 3
Hi,
I am wondering what mathematical formula is used to calculate growth of an investment if you have the percent return (or the doubling time of the investment). I could do it if there was a one time addition but what if you add a set amount each year (as in IRA contributions)?
Thanks,
Carson


I'm not sure which formula you are after? The amount you'll have in 10 years if your initial capital coumpounds at a 10% rate (A)? or the Rate of Return on your investment (B)?

For (A), you want to do the following calculation:
Final_value = Initial_value * (1+ Rate of Return)^Nb_years
(in Excel speak, FV = IV * POWER((1+RR), Nb_yrs)

For (B), you can use the following formula:
IRR(Value, Guess)
Here is the help Excel provides:

IRR(values,guess)

Values is an array or a reference to cells that contain numbers for which you want to calculate the internal rate of return.

Values must contain at least one positive value and one negative value to calculate the internal rate of return.


IRR uses the order of values to interpret the order of cash flows. Be sure to enter your payment and income values in the sequence you want.


If an array or reference argument contains text, logical values, or empty cells, those values are ignored.
Guess is a number that you guess is close to the result of IRR.

Microsoft Excel uses an iterative technique for calculating IRR. Starting with guess, IRR cycles through the calculation until the result is accurate within 0.00001 percent. If IRR can't find a result that works after 20 tries, the #NUM! error value is returned.


In most cases you do not need to provide guess for the IRR calculation. If guess is omitted, it is assumed to be 0.1 (10 percent).


If IRR gives the #NUM! error value, or if the result is not close to what you expected, try again with a different value for guess.

Examples

Suppose you want to start a restaurant business. You estimate it will cost $70,000 to start the business and expect to net the following income in the first five years: $12,000, $15,000, $18,000, $21,000, and $26,000. B1:B6 contain the following values: $-70,000, $12,000, $15,000, $18,000, $21,000 and $26,000, respectively.

To calculate the investment's internal rate of return after four years:

IRR(B1:B5) equals -2.12 percent

To calculate the internal rate of return after five years:

IRR(B1:B6) equals 8.66 percent

To calculate the internal rate of return after two years, you need to include a guess:

IRR(B1:B3,-10%) equals -44.35 percent



Did I answer your question?
UhuruPeak
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Your answer (A) is closer to what I want but not quite. Let me give 2 examples: 1st) (easier problem) Suppose that I start an IRA with an initial investment of $1000 and I want to know how much money I will have in 10 years or 20 years given an expected rate of return. I know the formula to use if I know how long it takes for my money to double:
Final value=initial value * 2^(time elapsed/doubling time)--- I think that this is an equivalent formula to yours for (A).

2nd) (and the one that I am trying to find a formula for) Suppose that I start an IRA with an initial investment of $1000 and every year I add $3000 more to it. What formula can I use to determine how much the IRA will be worth in a certain number of years given an expected rate of return. Also, in this case I would like to use percent expected return per year rather than doubling time. With the formula that you gave (answer A) I could do this by iterative means-calculating how much I earned in interest and adding my new annual investment and starting over with this as my initial value but I would like to avoid the brute force method if possible.

Thanks again,
Carson
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2nd) (and the one that I am trying to find a formula for) Suppose that I start an IRA with an initial investment of $1000 and every year I add $3000 more to it. What formula can I use to determine how much the IRA will be worth in a certain number of years given an expected rate of return.

You're looking for the future value of an annuity, which gets a little messier. One formula is:

((1+r)^n) - 1
-------------
r

where r is the expected rate of return (per period) and n is the number of periods.

That will work for the $3000 annual additions. Then you'll need to add in the value of your initial contribution of $1000 figured from the formula given to you earlier.

--Peter
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I've never been good with formulas. I belive that there is a caluculator at the below site that may help figure this out.


http://www.timevalue.com/tools.htm
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